Homogenization of two-phase elasto-plastic composite materials and structures: Study of tangent operators, cyclic plasticity and numerical algorithms

By I. Doghri, Amine Ouaar. 2003

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Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation (2004, methodology): “2 shows predictions of macro elastic modulus obtained with various homogenization models and with unit cell FE computations (described in Appendix A in Doghri and Ouaar [10]).”
Homogenization of elasto-(visco) plastic composites based on an incremental variational principle (2012, methodology): “For comparison, we also show results obtained with an incremental tangent method (Doghri and Ouaar, 2003; Pierard and Doghri, 2006b), labeled ‘‘Inc.Tgt’’ in the figures and briefly described in Appendix C.”
Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications (2010, background): “Recent developments in the incremental tangent formalism can be found, for instance, in [312,313].”
Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models (2004, background): “This limitation was overcome in successive tangent models by assuming proportional loading paths for each phase in the stress space, and hence an isotropic simpli)cation of the general, anisotropic form of tangent sti<ness tensor of each phase (Ponte Castañeda, 1996; Gonz. alez and LLorca, 2000; Dog”